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Academic literature on the topic 'Maximum Mean Discrepancy (MMD)'
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Journal articles on the topic "Maximum Mean Discrepancy (MMD)"
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Huang, Qihang, Yulin He, and Zhexue Huang. "A Novel Maximum Mean Discrepancy-Based Semi-Supervised Learning Algorithm." Mathematics 10, no. 1 (2021): 39. http://dx.doi.org/10.3390/math10010039.
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To provide more external knowledge for training self-supervised learning (SSL) algorithms, this paper proposes a maximum mean discrepancy-based SSL (MMD-SSL) algorithm, which trains a well-performing classifier by iteratively refining the classifier using highly confident unlabeled samples. The MMD-SSL algorithm performs three main steps. First, a multilayer perceptron (MLP) is trained based on the labeled samples and is then used to assign labels to unlabeled samples. Second, the unlabeled samples are divided into multiple groups with the k-means clustering algorithm. Third, the maximum mean discrepancy (MMD) criterion is used to measure the distribution consistency between k-means-clustered samples and MLP-classified samples. The samples having a consistent distribution are labeled as highly confident samples and used to retrain the MLP. The MMD-SSL algorithm performs an iterative training until all unlabeled samples are consistently labeled. We conducted extensive experiments on 29 benchmark data sets to validate the rationality and effectiveness of the MMD-SSL algorithm. Experimental results show that the generalization capability of the MLP algorithm can gradually improve with the increase of labeled samples and the statistical analysis demonstrates that the MMD-SSL algorithm can provide better testing accuracy and kappa values than 10 other self-training and co-training SSL algorithms.
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Zhou, Zhaokun, Yuanhong Zhong, Xiaoming Liu, Qiang Li, and Shu Han. "DC-MMD-GAN: A New Maximum Mean Discrepancy Generative Adversarial Network Using Divide and Conquer." Applied Sciences 10, no. 18 (2020): 6405. http://dx.doi.org/10.3390/app10186405.
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Generative adversarial networks (GANs) have a revolutionary influence on sample generation. Maximum mean discrepancy GANs (MMD-GANs) own competitive performance when compared with other GANs. However, the loss function of MMD-GANs is an empirical estimate of maximum mean discrepancy (MMD) and not precise in measuring the distance between sample distributions, which inhibits MMD-GANs training. We propose an efficient divide-and-conquer model, called DC-MMD-GANs, which constrains the loss function of MMD to tight bound on the deviation between empirical estimate and expected value of MMD and accelerates the training process. DC-MMD-GANs contain a division step and conquer step. In the division step, we learn the embedding of training images based on auto-encoder, and partition the training images into adaptive subsets through k-means clustering based on the embedding. In the conquer step, sub-models are fed with subsets separately and trained synchronously. The loss function values of all sub-models are integrated to compute a new weight-sum loss function. The new loss function with tight deviation bound provides more precise gradients for improving performance. Experimental results show that with a fixed number of iterations, DC-MMD-GANs can converge faster, and achieve better performance compared with the standard MMD-GANs on celebA and CIFAR-10 datasets.
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Xu, Haoji. "Generate Faces Using Ladder Variational Autoencoder with Maximum Mean Discrepancy (MMD)." Intelligent Information Management 10, no. 04 (2018): 108–13. http://dx.doi.org/10.4236/iim.2018.104009.
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Sun, Jiancheng. "Complex Network Construction of Univariate Chaotic Time Series Based on Maximum Mean Discrepancy." Entropy 22, no. 2 (2020): 142. http://dx.doi.org/10.3390/e22020142.
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The analysis of chaotic time series is usually a challenging task due to its complexity. In this communication, a method of complex network construction is proposed for univariate chaotic time series, which provides a novel way to analyze time series. In the process of complex network construction, how to measure the similarity between the time series is a key problem to be solved. Due to the complexity of chaotic systems, the common metrics is hard to measure the similarity. Consequently, the proposed method first transforms univariate time series into high-dimensional phase space to increase its information, then uses Gaussian mixture model (GMM) to represent time series, and finally introduces maximum mean discrepancy (MMD) to measure the similarity between GMMs. The Lorenz system is used to validate the correctness and effectiveness of the proposed method for measuring the similarity.
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Zhang, Xiangqing, Yan Feng, Shun Zhang, Nan Wang, Shaohui Mei, and Mingyi He. "Semi-Supervised Person Detection in Aerial Images with Instance Segmentation and Maximum Mean Discrepancy Distance." Remote Sensing 15, no. 11 (2023): 2928. http://dx.doi.org/10.3390/rs15112928.
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Detecting sparse, small, lost persons with only a few pixels in high-resolution aerial images was, is, and remains an important and difficult mission, in which a vital role is played by accurate monitoring and intelligent co-rescuing for the search and rescue (SaR) system. However, many problems have not been effectively solved in existing remote-vision-based SaR systems, such as the shortage of person samples in SaR scenarios and the low tolerance of small objects for bounding boxes. To address these issues, a copy-paste mechanism (ISCP) with semi-supervised object detection (SSOD) via instance segmentation and maximum mean discrepancy distance is proposed (MMD), which can provide highly robust, multi-task, and efficient aerial-based person detection for the prototype SaR system. Specifically, numerous pseudo-labels are obtained by accurately segmenting the instances of synthetic ISCP samples to obtain their boundaries. The SSOD trainer then uses soft weights to balance the prediction entropy of the loss function between the ground truth and unreliable labels. Moreover, a novel evaluation metric MMD for anchor-based detectors is proposed to elegantly compute the IoU of the bounding boxes. Extensive experiments and ablation studies on Heridal and optimized public datasets demonstrate that our approach is effective and achieves state-of-the-art person detection performance in aerial images.
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Zhao, Ji, and Deyu Meng. "FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test." Neural Computation 27, no. 6 (2015): 1345–72. http://dx.doi.org/10.1162/neco_a_00732.
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The maximum mean discrepancy (MMD) is a recently proposed test statistic for the two-sample test. Its quadratic time complexity, however, greatly hampers its availability to large-scale applications. To accelerate the MMD calculation, in this study we propose an efficient method called FastMMD. The core idea of FastMMD is to equivalently transform the MMD with shift-invariant kernels into the amplitude expectation of a linear combination of sinusoid components based on Bochner’s theorem and Fourier transform (Rahimi & Recht, 2007 ). Taking advantage of sampling the Fourier transform, FastMMD decreases the time complexity for MMD calculation from [Formula: see text] to [Formula: see text], where N and d are the size and dimension of the sample set, respectively. Here, L is the number of basis functions for approximating kernels that determines the approximation accuracy. For kernels that are spherically invariant, the computation can be further accelerated to [Formula: see text] by using the Fastfood technique (Le, Sarlós, & Smola, 2013 ). The uniform convergence of our method has also been theoretically proved in both unbiased and biased estimates. We also provide a geometric explanation for our method, ensemble of circular discrepancy, which helps us understand the insight of MMD and we hope will lead to more extensive metrics for assessing the two-sample test task. Experimental results substantiate that the accuracy of FastMMD is similar to that of MMD and with faster computation and lower variance than existing MMD approximation methods.
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Williamson, Sinead A., and Jette Henderson. "Understanding Collections of Related Datasets Using Dependent MMD Coresets." Information 12, no. 10 (2021): 392. http://dx.doi.org/10.3390/info12100392.
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Understanding how two datasets differ can help us determine whether one dataset under-represents certain sub-populations, and provides insights into how well models will generalize across datasets. Representative points selected by a maximum mean discrepancy (MMD) coreset can provide interpretable summaries of a single dataset, but are not easily compared across datasets. In this paper, we introduce dependent MMD coresets, a data summarization method for collections of datasets that facilitates comparison of distributions. We show that dependent MMD coresets are useful for understanding multiple related datasets and understanding model generalization between such datasets.
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Li, Kangji, Borui Wei, Qianqian Tang, and Yufei Liu. "A Data-Efficient Building Electricity Load Forecasting Method Based on Maximum Mean Discrepancy and Improved TrAdaBoost Algorithm." Energies 15, no. 23 (2022): 8780. http://dx.doi.org/10.3390/en15238780.
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Building electricity load forecasting plays an important role in building energy management, peak demand and power grid security. In the past two decades, a large number of data-driven models have been applied to building and larger-scale energy consumption predictions. Although these models have been successful in specific cases, their performances would be greatly affected by the quantity and quality of the building data. Moreover, for older buildings with sparse data, or new buildings with no historical data, accurate predictions are difficult to achieve. Aiming at such a data silos problem caused by the insufficient data collection in the building energy consumption prediction, this study proposes a building electricity load forecasting method based on a similarity judgement and an improved TrAdaBoost algorithm (iTrAdaBoost). The Maximum Mean Discrepancy (MMD) is used to search similar building samples related to the target building from public datasets. Different from general Boosting algorithms, the proposed iTrAdaBoost algorithm iteratively updates the weights of the similar building samples and combines them together with the target building samples for a prediction accuracy improvement. An educational building’s case study is carried out in this paper. The results show that even when the target and source samples belong to different domains, i.e., the geographical location and meteorological condition of the buildings are different, the proposed MMD-iTradaBoost method has a better prediction accuracy in the transfer learning process than the BP or traditional AdaBoost models. In addition, compared with other advanced deep learning models, the proposed method has a simple structure and is easy for engineering implementation.
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Lee, Junghyun, Gwangsu Kim, Mahbod Olfat, Mark Hasegawa-Johnson, and Chang D. Yoo. "Fast and Efficient MMD-Based Fair PCA via Optimization over Stiefel Manifold." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 7 (2022): 7363–71. http://dx.doi.org/10.1609/aaai.v36i7.20699.
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This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between the dimensionality-reduced conditional distributions of different protected classes. The incorporation of MMD naturally leads to an exact and tractable mathematical formulation of fairness with good statistical properties. We formulate the problem of fair PCA subject to MMD constraints as a non-convex optimization over the Stiefel manifold and solve it using the Riemannian Exact Penalty Method with Smoothing (REPMS). Importantly, we provide a local optimality guarantee and explicitly show the theoretical effect of each hyperparameter in practical settings, extending previous results. Experimental comparisons based on synthetic and UCI datasets show that our approach outperforms prior work in explained variance, fairness, and runtime.
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Han, Chao, Deyun Zhou, Zhen Yang, Yu Xie, and Kai Zhang. "Discriminative Sparse Filtering for Multi-Source Image Classification." Sensors 20, no. 20 (2020): 5868. http://dx.doi.org/10.3390/s20205868.
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Distribution mismatch caused by various resolutions, backgrounds, etc. can be easily found in multi-sensor systems. Domain adaptation attempts to reduce such domain discrepancy by means of different measurements, e.g., maximum mean discrepancy (MMD). Despite their success, such methods often fail to guarantee the separability of learned representation. To tackle this issue, we put forward a novel approach to jointly learn both domain-shared and discriminative representations. Specifically, we model the feature discrimination explicitly for two domains. Alternating discriminant optimization is proposed to obtain discriminative features with an l2 constraint in labeled source domain and sparse filtering is introduced to capture the intrinsic structures exists in the unlabeled target domain. Finally, they are integrated in a unified framework along with MMD to align domains. Extensive experiments compared with state-of-the-art methods verify the effectiveness of our method on cross-domain tasks.